Graph Using a Table of Values 3Y-2=3(X-3)

$3 Y - 2 = 3 (X - 3)$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$3 Y - 2 = 3 (X - 3)$

Step 2

Solve the equation for $y$ .

Simplify $3 (X - 3)$ .

Rewrite.

$3 Y - 2 = 0 + 0 + 3 (X - 3)$

Simplify by adding zeros.

$3 Y - 2 = 3 (X - 3)$

Apply the distributive property.

$3 Y - 2 = 3 X + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$3 Y - 2 = 3 X - 9$

Move all terms not containing $Y$ to the right side of the equation.

Add $2$ to both sides of the equation.

$3 Y = 3 X - 9 + 2$

Add $- 9$ and $2$ .

$3 Y = 3 X - 7$

Divide each term in $3 Y = 3 X - 7$ by $3$ and simplify.

Divide each term in $3 Y = 3 X - 7$ by $3$ .

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

Divide $Y$ by $1$ .

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $3$ .

Cancel the common factor.

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Divide $X$ by $1$ .

$Y = X + \frac{- 7}{3}$

Move the negative in front of the fraction.

$Y = X - \frac{7}{3}$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$3 Y - 2 = 3 (X - 3)$

Step 4

Solve the equation for $y$ .

Simplify $3 (X - 3)$ .

Rewrite.

$3 Y - 2 = 0 + 0 + 3 (X - 3)$

Simplify by adding zeros.

$3 Y - 2 = 3 (X - 3)$

Apply the distributive property.

$3 Y - 2 = 3 X + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$3 Y - 2 = 3 X - 9$

Move all terms not containing $Y$ to the right side of the equation.

Add $2$ to both sides of the equation.

$3 Y = 3 X - 9 + 2$

Add $- 9$ and $2$ .

$3 Y = 3 X - 7$

Divide each term in $3 Y = 3 X - 7$ by $3$ and simplify.

Divide each term in $3 Y = 3 X - 7$ by $3$ .

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

Divide $Y$ by $1$ .

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $3$ .

Cancel the common factor.

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Divide $X$ by $1$ .

$Y = X + \frac{- 7}{3}$

Move the negative in front of the fraction.

$Y = X - \frac{7}{3}$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$3 Y - 2 = 3 (X - 3)$

Step 6

Solve the equation for $y$ .

Simplify $3 (X - 3)$ .

Rewrite.

$3 Y - 2 = 0 + 0 + 3 (X - 3)$

Simplify by adding zeros.

$3 Y - 2 = 3 (X - 3)$

Apply the distributive property.

$3 Y - 2 = 3 X + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$3 Y - 2 = 3 X - 9$

Move all terms not containing $Y$ to the right side of the equation.

Add $2$ to both sides of the equation.

$3 Y = 3 X - 9 + 2$

Add $- 9$ and $2$ .

$3 Y = 3 X - 7$

Divide each term in $3 Y = 3 X - 7$ by $3$ and simplify.

Divide each term in $3 Y = 3 X - 7$ by $3$ .

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

Divide $Y$ by $1$ .

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $3$ .

Cancel the common factor.

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Divide $X$ by $1$ .

$Y = X + \frac{- 7}{3}$

Move the negative in front of the fraction.

$Y = X - \frac{7}{3}$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$3 Y - 2 = 3 (X - 3)$

Step 8

Solve the equation for $y$ .

Simplify $3 (X - 3)$ .

Rewrite.

$3 Y - 2 = 0 + 0 + 3 (X - 3)$

Simplify by adding zeros.

$3 Y - 2 = 3 (X - 3)$

Apply the distributive property.

$3 Y - 2 = 3 X + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$3 Y - 2 = 3 X - 9$

Move all terms not containing $Y$ to the right side of the equation.

Add $2$ to both sides of the equation.

$3 Y = 3 X - 9 + 2$

Add $- 9$ and $2$ .

$3 Y = 3 X - 7$

Divide each term in $3 Y = 3 X - 7$ by $3$ and simplify.

Divide each term in $3 Y = 3 X - 7$ by $3$ .

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

Divide $Y$ by $1$ .

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $3$ .

Cancel the common factor.

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Divide $X$ by $1$ .

$Y = X + \frac{- 7}{3}$

Move the negative in front of the fraction.

$Y = X - \frac{7}{3}$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$3 Y - 2 = 3 (X - 3)$

Step 10

Solve the equation for $y$ .

Simplify $3 (X - 3)$ .

Rewrite.

$3 Y - 2 = 0 + 0 + 3 (X - 3)$

Simplify by adding zeros.

$3 Y - 2 = 3 (X - 3)$

Apply the distributive property.

$3 Y - 2 = 3 X + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$3 Y - 2 = 3 X - 9$

Move all terms not containing $Y$ to the right side of the equation.

Add $2$ to both sides of the equation.

$3 Y = 3 X - 9 + 2$

Add $- 9$ and $2$ .

$3 Y = 3 X - 7$

Divide each term in $3 Y = 3 X - 7$ by $3$ and simplify.

Divide each term in $3 Y = 3 X - 7$ by $3$ .

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

Divide $Y$ by $1$ .

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $3$ .

Cancel the common factor.

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Divide $X$ by $1$ .

$Y = X + \frac{- 7}{3}$

Move the negative in front of the fraction.

$Y = X - \frac{7}{3}$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & X - \frac{7}{3} \\ - 1 & X - \frac{7}{3} \\ 0 & X - \frac{7}{3} \\ 1 & X - \frac{7}{3} \\ 2 & X - \frac{7}{3} \end{array}$

Step 12

Graph Using a Table of Values 3Y-2=3(X-3)

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